POD basis interpolation via inverse distance weighting on Grassmann manifolds. (English) Zbl 07097935

Mosquera, Rolando; Hamdouni, Aziz; El Hamidi, Abdallah; Allery, Cyrille

Discrete Contin. Dyn. Syst., Ser. S 12, No. 6, 1743-1759 (2019).

Summary: An adaptation of the Inverse Distance Weighting (IDW) method to the Grassmann manifold is carried out for interpolation of parametric POD bases. Our approach does not depend on the choice of a reference point on the Grassmann manifold to perform the interpolation, moreover our results are more accurate than those obtained in [7]. In return, our approach is not direct but iterative and its relevance depends on the choice of the weighting functions which are inversely proportional to the distance to the parameter. More judicious choices of such weighting functions can be carried out via kriging technics [23], this is the subject of a work in progress.

MSC:

65K05	Numerical mathematical programming methods
65D18	Numerical aspects of computer graphics, image analysis, and computational geometry
65F15	Numerical computation of eigenvalues and eigenvectors of matrices

Keywords:

proper orthogonal decomposition; sensitivity; compact operators